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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Multiplicity of
periodic solutions for Duffing equations
under nonuniform non-resonance conditions

Author: Chengwen Wang
Journal: Proc. Amer. Math. Soc. 126 (1998), 1725-1732
MSC (1991): Primary 34C25, 34B15
MathSciNet review: 1458269
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Abstract: This paper is devoted to the study of multiple $2 \pi$-periodic solutions for Duffing equations

\begin{equation*}x'' +cx' + g(t,x) = s(1+h(t)) \end{equation*}

under the condition of nonuniform non-resonance related to the positive asymptotic behavior of $g(t,x)x ^{-1}$ at the first two eigenvalues $0$ and $1$ of the periodic BVP on $[0,2 \pi]$ for the linear operator $L = - x''$, and the condition on the negative asymptotic behavior of $g(t,x)$ at infinity. The techniques we use are degree theory and the upper and lower solution method.

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Additional Information

Chengwen Wang
Affiliation: Department of Mathematics and Computer Science Rutgers University, Newark, New Jersey 07102

Received by editor(s): November 20, 1996
Communicated by: Hal L. Smith
Article copyright: © Copyright 1998 American Mathematical Society